3-DIMENSIONAL FREE-CONVECTION BOUNDARY-LAYERS IN POROUS-MEDIA INDUCEDBY A HEATED SURFACE WITH SPANWISE TEMPERATURE-VARIATIONS

In this paper we consider the effect of a nonuniform surface temperatu re distribution on the steady laminar free convection boundary layer f low induced by a vertical plate embedded in a fluid-saturated porous m edium. The surface temperature profile exhibits sinusoidal variations in the spanwise (horizontal) direction, but the minimum temperature re mains above or equal to that of the ambient medium. The resulting boun dary layer flow is three-dimensional, and the governing equations are solved using a combination of a spanwise spectral decomposition and th e Keller-box method. Detailed results in terms of the evolution of the rates of heat transfer and the developing thermal field are presented . The numerical work is supplemented by an asymptotic analysis valid f ar downstream where it is found that the effect of nonuniform heating becomes confined to a thin layer of uniform thickness embedded within the main growing boundary layer.